Fourier-reflexive partitions and MacWilliams identities for additive codes

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18 Scopus citations

Abstract

A partition of a finite abelian group gives rise to a dual partition on the character group via the Fourier transform. Properties of this dualization are investigated, and a convenient test is given for when the bidual partition coincides with the primal partition. Such partitions permit MacWilliams identities for the partition enumerators of additive codes. It is shown that dualization commutes with taking products and symmetrized products of partitions on cartesian powers of the given group. After translating the results to Frobenius rings, which are identified with their character module, the approach is applied to partitions that arise from poset structures.

Original languageEnglish
Pages (from-to)543-563
Number of pages21
JournalDesigns, Codes, and Cryptography
Volume75
Issue number3
DOIs
StatePublished - Jun 1 2015

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

  • Dualization
  • Partitions
  • Poset structures
  • Weight enumerators

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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